Which statement correctly describes the purpose of solving f(x)=g(x) when computing ∫ab(g(x)−f(x))dx for the area enclosed by y=f(x) and y=g(x)?
a) It reveals which function lies above the other throughout the interval, guaranteeing the integrand g(x)−f(x) is non-negative.
b) It determines the x-coordinates of the intersection points, which serve as the limits a and b of the integral.
c) It gives the vertical distance between the curves at every x, which is then integrated to find the area.
d) It guarantees that g(x)−f(x) is positive on the chosen interval because its sign can change only at those solutions.